Probability Theory and Mathematical Statistics

Bachelor 2024/2025

Type: Compulsory course (International Business)

Area of studies: Management

Delivered by: Department of Strategic and International Management

Where: Graduate School of Business

When: 1 year, 3, 4 module

Mode of studies: offline

Open to: students of one campus

Instructors: Margarita Gladkova, Gleb Karpov

Language: English

ECTS credits: 4

Full Syllabus Ask Question

Abstract

This is second half of the course Probability Theory and Mathematical Statistics which is a core mathematical subject and is dedicated to statistical part of the course. The statistical section starts with the descriptive techniques but quickly switches to the inferential methods. The topics covered here include sampling distributions, point and interval estimates, hypothesis testing. We conclude with a univariate and, if time permits, multivariate regression. This course is the basis for the development of students' skills in probabilistic and statistical thinking, needed for analysis and modeling in management.

Learning Objectives

be able to summarise the ideas of randomness and variability, and the way in which these link to probability theory
• Be able to process the empirical data; .
have a grounding in probability theory
• Be able to apply statistical methods to solve applied managerial problems;
be able to solve typical probabilistic problems
• Be familiar with Microsoft Office programs for empirical data processing

Expected Learning Outcomes

Be able to build, assess the quality and make predictions with the linear regression model.
Be able to derive and use the main sampling distributions - for mean, proportion and variance
Be able to estimate the main characteristics of a random variable by means of point or interval estimates. Know how to construct and interpret the confidence intervals for mean, proportion and variance.
Be able to use the concept of conditional probability, law of total probability, notion of independence, collectively exhaustive events.
Be able to use the methods of descriptive statistics to summarize and visualize the raw data.
Be aware of different definitions of probability, the axioms of probability and their use for derivation of major probabilistic relationships. Know the basic counting methods and principles of combinatorics.
Know and be able to use alternative ways of describing a continuous random variable - probability density function and cumulative distribution function. Know how to calculate basic characteristics of a continuous random variable. Be aware of commonly used continuous distributions.
Know how to work with a multivariate random variable using the joint probability distribution. Be able to detect the indepedent random variables, calculate the marginal and conditional distributions, covariance and correlation between the variables.
Understand the principles of hypothesis testing. Be able to perform tests for population mean, proportion and variance.
Understand what is meant by a random variable. Know how to use the probability mass functions for calculating the basic characteristics of a discrete random variable (expected value, variance). Be aware of commonly used discrete distributions.

Course Contents

Axioms of probability
Conditional probability and independence
Discrete random variables
Continuous random variables
Jointly distributed random variables
Ideas of sampling and sampling distributions
Point and interval estimates
Hypothesis testing
Linear regression model

Assessment Elements

Home Assignment in Probability Theory
Home Assignment is Mathematical Statistics
Quiz in Probability Theory
Short synchronous or asynchronous quizzes. Each quiz takes 10-15 minutes from starting an attempt and covers the material of the previous topics. Question types might be a multiple-choice, short answer, or uploading a photo of hand-written solution.
Quiz in Mathematical Statistics
Mid-term Exam in Probability Theory
Final Exam

Interim Assessment

2024/2025 4th module
0.3 * Final Exam + 0.15 * Home Assignment in Probability Theory + 0.15 * Home Assignment is Mathematical Statistics + 0.2 * Mid-term Exam in Probability Theory + 0.1 * Quiz in Mathematical Statistics + 0.1 * Quiz in Probability Theory

Bibliography

Recommended Core Bibliography

9780429766749 - Blitzstein, Joseph K.; Hwang, Jessica - Introduction to Probability, Second Edition - 2019 - Chapman and Hall/CRC - http://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=2024519 - nlebk - 2024519
Biswas, D. (2019). Probability and Statistics: Volume I. [N.p.]: New Central Book Agency. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2239779

Recommended Additional Bibliography

Balakrishnan, N., Koutras, M. V., & Konstantinos, P. (2019). Introduction to Probability : Models and Applications. Hoboken, NJ: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2097342
Ghahramani, S. (2018). Fundamentals of Probability : With Stochastic Processes (Vol. Fourth edition). Boca Raton, FL: Chapman and Hall/CRC. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1875108
Linde, W. (2017). Probability Theory : A First Course in Probability Theory and Statistics. [N.p.]: De Gruyter. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1438416
Linton, O. B. (2017). Probability, Statistics and Econometrics. London, United Kingdom: Academic Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1200673

Authors

KARPOV GLEB ALEKSANDROVICH

Course Syllabus